radio frequency circuit design

Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9CHAPTER ONE Communication Channel 1.1 BASIC TRANSMITTER–RECEIVER CONFIGURATION The design of radio frequency RF circuits borrows fro

Copyright  2001 John Wiley & Sons, Inc Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

Radio Frequency

Circuit Design

KAI CHANG, Editor

Texas A&M University

A complete list of the titles in this series appears at the end of this volume

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Library of Congress Cataloging-in-Publication Data:

Davis, W Alan.

Radio frequency circuit design / W Alan Davis, Krishna Agarwal.

p cm — (Wiley series in microwave and optical engineering)

Includes index.

ISBN 0-471-35052-4

1 Radio circuits — Design and construction I Agarwal, Krishna K (Krishna Kumar)

II Title III Series.

TK6560 D38 2001

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

Margaret Davis, Elisabeth Agarwal

and our children:

Brent, Nathan, Janelle DavisSareeta, Sandeep, Suneet Agarwal

1.1 Basic Transmitter–Receiver Configuration 1

3.9 Parallel Double-Tuned Transformer 45

vii

4.1 Voltage–Current Two-Port Parameters 51

4.5 The Transmission Line Equation 61

4.7 Commonly Used Transmission Lines 65

5.6 Matching between Unequal Resistances 95

8.5 Amplifier Noise Characterization 151

8.8 Two-Port Noise Figure Derivation 1548.9 The Fukui Noise Model for Transistors 1588.10 Properties of Cascaded Amplifiers 1618.11 Amplifier Design for Optimum Gain and Noise 164

10.3 Two-Port Oscillators with External Feedback 197

10.5 Minimum Requirements of the Reflection Coefficient 20410.6 Common Gate (Base) Oscillators 206

11.1 Nonlinear Device Characteristics 222

12.7 Linear Analysis of the PLL [1] 255

D Two-Port Parameter Conversion 292

E Termination of a Transistor Port with a Load 296

F Transistor and Amplifier Formulas 300

G Transformed Frequency Domain Measurements

H Single-Tone Intermodulation Distortion

Suppression for Double-Balanced Mixers 319

The cellular telephone has become a symbol for the rapid change in the nications business Within this plastic container reside the talents of engineersworking in the areas of efficient power supplies, digital circuit design, analogcircuit design, semiconductor device design, antennas, linear systems, digitalsignal processing, packaging, and materials science All these talents are carefullycoordinated at a cost that allows a wide cross section of the world’s population tohave available instant communication The particular aspect of all these activitiesthat is of primary focus in this text is in the area of analog circuit design, withprimary emphasis on radio frequency electronics Some topics normally consid-ered in electronics courses or in microwave and antenna courses are not coveredhere For example, there is no mention of distributed branch line couplers, since

commu-at 1 GHz their size would be prohibitive On the other hand, topics such as mission line transformers are covered because they fit so well into this frequencyrange

trans-This book is meant for readers who have at least advanced standing in trical engineering The material in this text has been taught as a senior andgraduate-level course in radio frequency circuit design at the University of Texas

elec-at Arlington This class has continued to be popular for the past 20 years underthe guidance of at least four different instructors, two of whom are the presentauthors Because of the activity in the communications area, there has been evergreater interest in this subject It is the intent of the authors, therefore, to updatethe current text offerings while at the same time avoiding simply reworking amicrowave text

The authors gratefully acknowledge the contribution of Michael Black,Raytheon Systems Company, to the phase lock loop discussion in Chapter 12

W Alan DavisKrishna Agarwal

Copyright  2001 John Wiley & Sons, Inc Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

Actual noise figure, 151

Admittance parameters, see y parameters

Porcelain, 16 – 17 Capacity, 3, 5 – 7 Cascaded amplifiers, 161 Cauer extraction, 97 CDMA, 3, 279 – 280, 282 Channel, 4

Characteristic admittance, 154 Characteristic impedance, 61 – 62, 65, 67,

72 – 73, 77 – 78, 102 – 103, 106, 114,

119 – 120, 154, 205, 289, 294, 306, 309

CHEBY, 102 Chebyshev, 90 – 92, 94 – 96, 98, 102 Circuit Q, 33, 44

Class A amplifier(s), 3, 122, 168, 181 Class A power amplifier(s), 139 Class AB amplifier(s), 3 Class B amplifier(s), 169 – 171, 173,

175 – 177, 181 Class C amplifier(s), 3, 178 – 179,

181 – 183, 188 Class D amplifier, 184 Class F amplifier, 185 – 186, 188 Coaxial transmission line, 67 – 68, 115 Collector efficiency, 185

Combiner(s), 117 – 118 Combining, power 141 – 142 COMSAT, 283

Conduction angle, 169, 170, 178 – 179,

183 – 184 Conductivity, 9 – 10 Conductor loss, 70 – 71, 73 Conversion compression, 227, 242

Fukui equations, 161 Fukui noise model, 158

g parameters, 52, 74, 132, 197, 292 Generators, harmonic, 216

GMSK, 279 GPRS, 282 Group delay, 85 – 86 Group velocity, 62 GSM, 278, 282

h parameters, 51, 74, 132, 197, 292 HALO, 283

Harmonic generators, see Multiplier(s) Hybrid coupler, 118

Ideal transformer, 46 – 47, 105, 306 Image frequency, 224, 244 – 245 Image impedance, 54 – 57, 59 Image propagation constant, 57 – 58 Impedance match(ing), 36, 95, 141

Impedance parameters, see z parameters

Impedance transformation, 105, 121 Impedance transformer, 120 IMSUP, 240, 319, 321 IMT-2000, 279 Indefinite admittance matrix, 78 – 79,

207, 298 Indefinite scattering matrix, 80, 82 Inductor(s)

circular spiral, 26 ferrite(s), 22 – 23 microstrip, 26 monolithic, 26 proximity effect, 22 self resonance, 21 spiral, 26 – 28, 30, 286 loss, 20, 22

Information, 1, 3 – 7 Injection locking range, 216 Input intercept point, 227 Insertion gain, 122 INTEL-SAT, 283

Noise figure, 122, 151 – 154, 157,

161 – 162, 164 – 165, 227, 243 – 244 double-sideband, 244, 246

single-sideband, 243 – 246 Noise measure, 152 Noise temperature, 151 – 152, 243 – 244 Noise, 1, 155, 191 – 192, 201, 204,

210, 230 flicker, 3, 144 Johnson, 144 minimum, 201, 203 Nyquist, 144 shot, 148 – 149 spot, 151 Nyquist formula, 147, 149, 151

Odd mode voltage, 28 – 29 Odd-mode current, 106 – 107 Ohmic contact, 13

Op-amp, see Operational amplifier(s)

Open loop gain, 201, 262 Operational amplifier(s), 247 – 249, 254,

258 – 259, 262, 267, 272 Oscillator(s)

Armstrong, 197 – 198 Clapp-Gouriet, 197 – 199 Colpitts, 197 – 200, 202 Hartley, 197 – 198, 202 – 203 injection-locked, 214 Pierce, 197 – 198 Vackar, 197 – 199 voltage controlled, 199, 206, 249 – 254,

256, 259 – 264, 270 – 272, 275

 circuit, 39 – 41, 45 PACS, 279

Parallel plate line, 66 PARCONV, 292, 294 Phase detector(s), 247, 249, 250 – 254,

259 – 264, 271 – 272, 274 – 275 flip-flop, 272 – 273

sampling, 270 – 272 Phase error, 257 – 259 Phase margin, 247, 250 Phase velocity, 62 PLMR, 278 POLY, 97 Positive real, 96 Power amplifier(s), 3, 141, 191, 281 Power gain, 122

Scattering matrix, see S parameter(s)

Scattering parameters, see S parameter(s)

Tapped C, see Tapped capacitor

Tapped capacitor, 42 – 45 TDMA, 3, 278, 280, 282

TDR, see Time domain reflectometer

Telegrapher’s equation(s), 59 – 61, 63,

65 – 66 Temperature coefficient, 11, 74 Thompson-Bessel, 93, 96 Time domain reflectometer, 305 – 306,

308, 313 Transducer power gain, 89, 123 – 124,

126, 243 Transient(s), 204, 210, 247, 264 Transmission coefficient, 74, 77 – 78 Transmission line equation, 61, 63 Transmission line(s), 59 – 62, 65 – 66, 71,

106 – 116, 118 – 121, 132, 305, 310 Two-wire line, 65 – 66

Type 1 PLL, 254, 259, 262, 265, 267, 276 Type 2 PLL, 254, 262, 265, 267, 270, 275

Type 3 PLL, 262

UHF, 278 Unilateral amplifiers, 162, 164 approximation, 164 power gain, 126 – 127 Unloaded Q, 36

VCO, see Oscillator(s)

Y factor, 152 – 153

z parameters, 51 – 54, 56, 74, 123, 132,

197, 292, 294

16QAM, 281 1G, 282 2G, 282 3G, 279, 282 4G, 279 64QAM, 281

Copyright  2001 John Wiley & Sons, Inc Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING

KAI CHANG, Editor

Texas A&M University

FIBER-OPTIC COMMUNICATION SYSTEMS, Second Edition

Govind P Agrawal

COHERENT OPTICAL COMMUNICATIONS SYSTEMS

Silvello Betti, Giancarlo De Marchis and Eugenio Iannone

HIGH-FREQUENCY ELECTROMAGNETIC TECHINQUES: RECENT ADVANCES AND

DIODE LASERS AND PHOTONIC INTEGRATED CIRCUITS

Larry Coldren and Scott Corzine

MULTICONDUCTOR TRANSMISSION-LINE STRUCTURES: MODAL ANALYSIS TECHNIQUES

FUNDAMENTALS OF WAVELETS: THEORY, ALGORITHMS, AND APPLICATIONS

Jaideva C Goswami and Andrew K Chan

K C Gupta and Peter S Hall

PHASED ARRAY ANTENNAS

R C Hansen

HIGH-FREQUENCY ANALOG INTEGRATED CIRCUIT DESIGN

Ravender Goyal (ed.)

MICROWAVE APPROACH TO HIGHLY IRREGULAR FIBER OPTICS

Huang Hung-Chia

NONLINEAR OPTICAL COMMUNICATION NETWORKS

Eugenio Iannone, Franceso Matera, Antonio Mecozzi, and Marina Settembre

FINITE ELEMENT SOFTWARE FOR MICROWAVE ENGINEERING

Tatsuo Itoh, Giuseppe Pelosi and Peter P Silvester (eds.)

INFRARED TECHNOLOGY: APPLICATIONS TO ELECTRO-OPTICS, PHOTONIC DEVICES, AND SENSORS

A R Jha

SUPERCONDUCTOR TECHNOLOGY: APPLICATIONS TO MICROWAVE, ELECTRO-OPTICS, ELECTRICAL MACHINES, AND PROPULSION SYSTEMS

A R Jha

OPTICAL COMPUTING: AN INTRODUCTION

M A Karim and A S S Awwal

INTRODUCTION TO ELECTROMAGNETIC AND MICROWAVE ENGINEERING

Paul R Karmel, Gabriel D Colef, and Raymond L Camisa

MILLIMETER WAVE OPTICAL DIELECTRIC INTEGRATED GUIDES AND CIRCUITS

Shiban K Koul

MICROWAVE DEVICES, CIRCUITS AND THEIR INTERACTION

Charles A Lee and G Conrad Dalman

ADVANCES IN MICROSTRIP AND PRINTED ANTENNAS

Kai-Fong Lee and Wei Chen (eds.)

OPTICAL FILTER DESIGN AND ANALYSIS: A SIGNAL PROCESSING APPROACH

Christi K Madsen and Jian H Zhao

OPTOELECTRONIC PACKAGING

A R Mickelson, N R Basavanhally, and Y C Lee (eds.)

OPTICAL CHARACTER RECOGNITION

Shunji Mori, Hirobumi Nishida, and Hiromitsu Yamada

ANTENNAS FOR RADAR AND COMMUNICATIONS: A POLARIMETRIC APPROACH

Harold Mott

INTEGRATED ACTIVE ANTENNAS AND SPATIAL POWER COMBINING

Julio A Navarro and Kai Chang

ANALYSIS METHODS FOR RF, MICROWAVE, AND MILLIMETER-WAVE PLANAR

TRANSMISSION LINE STRUCTURES

Cam Nguyen

FREQUENCY CONTROL OF SEMICONDUCTOR LASERS

Motoichi Ohstu (ed.)

SOLAR CELLS AND THEIR APPLICATIONS

Larry D Partain (ed.)

ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES

Clayton R Paul

Clayton R Paul

ELECTROMAGNETIC OPTIMIZATION BY GENETIC ALGORITHMS

Yahya Rahmat-Samii and Eric Michielssen (eds.)

INTRODUCTION TO HIGH-SPEED ELECTRONICS AND OPTOELECTRONICS

Leonard M Riaziat

NEW FRONTIERS IN MEDICAL DEVICE TECHNOLOGY

Arye Rosen and Harel Rosen (eds.)

ELECTROMAGNETIC PROPAGATION IN MULTI-MODE RANDOM MEDIA

InP-BASED MATERIALS AND DEVICES: PHYSICS AND TECHNOLOGY

Osamu Wada and Hideki Hasegawa (eds.)

DESIGN OF NONPLANAR MICROSTRIP ANTENNAS AND TRANSMISSION LINES

Kin-Lu Wong

FREQUENCY SELECTIVE SURFACE AND GRID ARRAY

T K Wu (ed.)

ACTIVE AND QUASI-OPTICAL ARRAYS FOR SOLID-STATE POWER COMBINING

Robert A York and Zoya B Popovi´c (eds.)

OPTICAL SIGNAL PROCESSING, COMPUTING AND NEURAL NETWORKS

Francis T S Yu and Suganda Jutamulia

SiGe, GaAs, AND InP HETEROJUNCTION BIPOLAR TRANSISTORS

Jiann Yuan

ELECTRODYNAMICS OF SOLIDS AND MICROWAVE SUPERCONDUCTIVITY

Shu-Ang Zhou

Copyright  2001 John Wiley & Sons, Inc Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

CHAPTER ONE

Communication Channel

1.1 BASIC TRANSMITTER–RECEIVER CONFIGURATION

The design of radio frequency (RF) circuits borrows from methods used in frequency audio circuits as well as from methods used in design of microwavecircuits Yet there are also important departures from these techniques, so thedesign of radio frequency circuits requires some specialized techniques not found

low-in these other frequency ranges The radio frequency range for present purposeswill be taken to be somewhere between 300 MHz and 3 GHz It is this frequencyrange where much of the present day activity in wireless communication occurs

In this range of frequencies, the engineer must be concerned about radiation,stray coupling, and frequency response of circuit elements that from the point

of view of lumped, low-frequency analysis might be expected to be dent of frequency At the same time the use of common microwave circuitelements such as quarter wave transformers is impractical because of the longline lengths required The use of monolithic circuits have enabled many high-frequency designs to be implemented with lumped elements, yet the frequencyresponse of these “lumped” elements still must be carefully considered

indepen-Today RF and digital designs have begun to move closer together, so typicalcommunication systems incorporate both of these disciplines in their design Whiledirect digitizing of RF signals remains a challenge, there are many systems wheredigital signal processing is playing a larger role than ever in communication systems

A typical radio analog transmitter and receiver is shown in Fig 1.1 In this systemthe information source could be an audio or video signal This information in theprocess of being converted from, say, sound to an electrical signal by a transducerproduces a very low voltage that must be amplified by an audio amplifier

The modulator is shown schematically as a mixer that represents a widevariety of different modulation schemes The two major categories are analogand digital modulation In either case the modulator performs two functions Thefirst function is that it encodes the message in a certain way so as to meet thecommunication channel requirements for cost, noise immunity, fading, available

1

bandwidth, bandwidth efficiency (the ratio of the throughput data rate per Hertz

in a given bandwidth), power efficiency (which measures the ability of a system

to preserve the message under low power conditions), and so on

For the amplitude modulation (AM) case, the mixer is a multiplier thatmultiples the information message with the local oscillator frequency Just

as the product of two sine waves produces sum and difference frequencies,

so the message frequency is added to the local oscillator frequency Thisproduces two effects necessary for practical wireless communications The first

is that this enables forming multiple channels, which in the amplitude andfrequency modulation (FM) analog systems are separated by different frequencybands Otherwise, there would be massive interference between different signals.This method of separating signals is called frequency division multiple access(FDMA) Alternate methods are time division multiple access (TDMA) wheretwo or more signals may share the same frequency band but use it at differenttimes The human receiver is able to integrate over the different time slots so thatthe message is perceived to be continuous A third method is the spread spectrumtechnique known as code division multiple access (CDMA) where a broadbandwidth is used by multiple users continuously However, each user sendsand receives data that is coded in a particular way, different from all the otherusers When there is interference between users, it is perceived as low-level noise.The second function of the modulator is that it translates the message infor-mation to a much higher RF signal For this reason antennas can be made amanageable size, with their mechanical size normally correspondings to the wave-length A great deal of effort has gone into making smaller antennas, but thereare always design compromises

The final stage of the transmitter before reaching the antenna is the poweramplifier Since this component uses the greatest amount of power, high effi-ciency becomes an important factor In FM systems, class C amplifiers are oftenused because, in practice, they can produce efficiencies as high as 70% For

AM systems, class A or AB amplifiers are often used because of the requiredlinearity of AM signal transmission However, class A amplifiers typically haveefficiencies of 30% to 40%

As for the receiver, the received signal is sometimes strong enough to beput directly into the mixer However, as will be seen later (in Chapter 8), theoverall noise response of the amplifier is greatly enhanced by using a low-noiseamplifier for the front end The demodulator in the receiver must correspond

to the modulator in the transmitter The subsequent intermediate frequency (IF)amplifier includes the required filtering to provide the desired selectivity for thereceived signal The IF frequency is chosen to be sufficiently high to avoid most

of the 1/f noise (f D frequency) or flicker noise Since this circuit operates at

a fixed frequency, it can be carefully tuned for optimum performance

1.2 INFORMATION AND CAPACITY

RF communication systems provide a means of carrying information from

the transmitter to the receiver Now, what exactly is information? Webster’s

Dictionary states that “information” is “knowledge communicated or received

concerning a particular fact or circumstance ” A narrower, technical definitionthat more closely aligns with our focus that “information” is an “indication

of the number of possible choices of messages, which are expressible as thevalue of some monotonic function of the number of choices, usually log to thebase 2.” “Information” then is a term for data that can be coded for digitalprocessing

Some examples of data that illustrate the meaning of information is helpful If

a signal were sent through a communication channel that never changed, then itwould be conveying no information There must be change to convey a message

If the signal consisted of 1 0 1 0 1 0 1 0 , there would be changes in the signalbut still no information is conveyed, because the next bit would be perfectlypredictable So while change is important, it is not the sole criterion for informa-tion There is one last example If a signal in an amplitude modulation systemconsists of purely random voltage fluctuations, then again no information can betransmitted It is simply noise, and the receiver becomes no more knowledgeableupon having heard it

A communication system consists of a transmitter, a receiver, and a channel.The channel is capable of carrying only a certain limited amount of information.Roughly analogous to an information channel is a water pipe which, because of itsdiameter, is restricted to carrying only a certain amount of water This limitation

is given the technical term “capacity.” It refers to the amount of informationthat is transmitted over a time interval of T seconds The time interval can

be broken up into shorter time intervals, each of duration  Clearly, the moredistinct time intervals  these are in the total time span T, the more informationcan be transmitted The minimum size of  is determined by how well onepulse in one time frame can be distinguished from a pulse in a neighboring timeframe The limitation on how short a time frame can be is related to the channelbandwidth

In addition the signal voltage will have a maximum amplitude that is limited bythe available power in the system This voltage range can be divided into manylevels, each level representing a bit of information that is distinguished fromanother bit The voltage range cannot be infinitely split because of the noise that

is always present in the system Clearly, the more voltage intervals there are

in a given time frame , the more information capacity there is in the system.Just as the flow of water through a pipe is limited by the amount of pressure onthe water, by the friction on the walls of the pipe, and by the diameter of thepipe, so the capacity of a transmission system is limited by the maximum voltagelevel, by the noise in the system that tends to muddle the distinction between onevoltage level and another, and by the bandwidth of the channel, which is related

to the rise time of a pulse in the system

In one of the time intervals, , there are n voltage levels The smaller that  isand the larger that n is, the more information there can be transmitted through thechannel In each time interval there are n possible voltage levels In the next timeinterval there are also n possible voltage levels It is assumed that the voltage

level in each time frame is independent of what is going on in other time frames.The amount of information transmitted in a total of T seconds corresponds to theproduct of the possible levels in each interval:

n Ð n Ð n Ð n nT/ 1.1 The total information transmitted intuitively is directly proportional to the totaltime span T, which is defined as the log of the above product By convention,the base-2 logarithm is used

of voltage levels increases, so does the capacity for more information

Information can be transmitted through a channel in a variety of differentforms, all producing the same amount of information For example, supposethat a signal can take on any one of eight different voltage levels, 0, 1, ,

7, in a given time interval  But the eight signal levels could also equally besent with just two levels, 0, 1 For every interval that has eight possible levels,three intervals will be needed for the two-level signal A convenient conversionbetween the two systems is shown in Table 1.1

Clearly, a 16-level signal could be transmitted by a sequence of four binarysignals, and a 32-level signal with a sequence of five binary signals, and so

on For n levels, log2n bits are needed The information content of a signal

is defined then to be the number of binary choices, or bits, that are needed

TABLE 1.1 Eight-Level and Two-Level Systems

for transmission A system is designed to transmit speech must be designed tohave the capacity to transmit the information contained in the speech Whilespeech is not entirely what humans communicate, in a communication system

it is what engineers have to work with A decision must be made as to withwhat fidelity the speech is to be transmitted This translates to the bandwidthrequirement of an analog system, or the number of voltage levels available in

a given total voltage range Ultimately this restriction is always present even

if sophisticated coding techniques are used The capacity of the system must

be ½, the rate of information that is to be transmitted Beyond this capacity,system cost, power levels, and available transmission media must beconsidered

1.3 DEPENDENT STATES

The definitions of the preceding section imply that the voltage level in each timeinterval, , is independent of the voltage level in other time intervals However,one simple example where this is not the case is the transmission of the Englishlanguage It is known that in the English language the letter e appears morefrequently than the letter z It is almost certain that the letter q will be followed

by the letter u So, in transmitting a typical message in English, less information

is actually sent than would be sent if every letter in the alphabet were equallylikely to occur A way to express this situation is in terms of probability Weare interested in the total number of signal combinations that could occur in

a message T seconds long if each interval that is independent from the others

is nT/ On average, every possible message T seconds long would have aprobability of occurrence of 1/nT/

The probability takes the form

P D number of occurrences of a particular event

total number of events 1.4 For information measured in terms of probability, P D 1/n if there are n eventsspecified as n voltage levels and each of these events is equally likely For anyone event, the information transmitted is written H1 D log2P For m intervals,each  seconds long, there will be m times more information So for m intervals,the information written in terms of probability is

H D T

 log2n D mlog2P bits 1.5 Consider a binary system where a number 0 occurs with probability p and thenumber 1 occurs with probability q Knowing that p C q D 1, the informationcontent of a message consisting of 0’s and 1’s is to be found The total information

is the sum of the information carried by the 0’s and that of the 1’s:

H D T

p Ðlog2p C q Ðlog2q bits 1.6

If the probabilities of p and q are each 0.5, then the total information in Tseconds is T/ If, for example, p D 0.25 and q D 0.75, then

Hence, when there is a greater probability that an expected event will occur, there

is less information As p approaches 1 and q approaches 0, the near certainty

of event with probability p will give 0 information The maximum informationoccurs when p D q D 0.5

This scenario can be generalized for n signal levels in a given signal interval

 Assume that each of these n signal levels, si, has a probability of occurrence

of Pi where

P1CP2C Ð Ð Ð CPnD

Assume further that the probability of a finding a given signal level is independent

of the value of the adjacent signal levels The total information in T/ intervals

Pilog2PiD T

 log2n bits 1.11

More detail on information transmission can be found in specialized texts;

a short introduction is given by Schwartz [1] In general, this study of radiofrequency design, the primary focus will be on fundamental hardware design used

in transmitters and receivers Other topics that are of great interest to tion engineers such as programming digital signal processing chips, modulationschemes, and electromagnetic propagation problems are more fully explored in

communica-specialized texts in those areas In this book these areas will be referred to only

as needed in illustrations of how systems can be implemented

PROBLEMS

1.1 A pulse train is being transmitted through a channel at the maximum channel

capacity of 25 Ð 103 bits/s The pulse train has 16 levels

(a) What is the pulse width?

(b) The pulse width is doubled and sent back on the same channel What is

number of levels required?

REFERENCES

1 M Schwartz, Information Transmission, Modulation, and Noise, 3rd ed., New York:

McGraw-Hill, 1980, Ch 1.

Copyright  2001 John Wiley & Sons, Inc Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

care-in high-frequency circuits Usually the “lumped” element is best modeled as

a combination of these pure elements In addition, when the size of the elementbecomes larger than 0.1 wavelength in the circuit medium, the equivalent circuitshould include the transmission lines

2.2 RESISTORS

Integrated circuit resistors can be classified into three groups: (1) semiconductorfilms, (2) deposited metal films, and (3) cermets (a mixture of metal and dielectricmaterials) Of these, only the first two have found widespread use in high-frequency circuits Semiconductor films can be fabricated by diffusion into a hostsemi-insulating substrate, by depositing a polysilcon layer, or by ion implanta-tion of impurities into a prescribed region Polysilcon, or polycrystalline silicon,consists of many small submicron crystals of silicone with random orientations

2.2.1 Resistor Types

The resistance value of an integrated circuit resistor depends on the conductivity

of the channel through which the current is flowing In the diffused resistors in asemiconductor substrate, the conductivity is a function of the doping concentration

9

and the carrier mobility The conductivity is

D qnn C pp 2.1

It is usually expressed in the units of   cm1 In this expression, q is theelectronic charge 1.602 Ð 1019 C, n and p are the electron and hole mobil-ities (cm2/V  s), and n and p are the number of free electrons and holes,respectively, that are available for conduction (cm3) At room temperature itmay be assumed that all the impurity atoms in the semiconductor are ionized.This means that for an n-type semiconductor, the number of available electrons

is equal to the donor impurity concentration:

where niD1.45 Ð 1010 cm3for silicon and 9.0 Ð 106for gallium arsenide This is

called the mass action law Thus, for an n-type semiconductor, the conductivity is

D q

nNDCpn

2 i

ND



³qnND 2.5Typically, in integrated circuits, n-channel FETs and NPN bipolar transistors arepreferred because of the much larger electron mobility over that of the holemobility The total number of processing steps required in a circuit design oftendictates the choice of resistor channel type

Ideally the diffused resistor with conductivity
can be represented by therectangular block shown in Fig 2.1 The resistance of the rectangular block is

W

L

FIGURE 2.1 Diffused resistor of length L, width W, height T.

TABLE 2.1 Resistor Materials

Resistor Type Resistance Temperature Coefficient Voltage Coefficient

in temperature and voltage Table 2.1 shows some of the main properties of avariety of methods and materials The temperature and voltage coefficients aremeasures of the percentage change in resistance as a function of a change in agiven parameter The definition of temperature coefficient is dR/dT/R and the

voltage coefficient is d R/d V/R.

2.2.2 Resistance Determination from Layout

The layout shape of a resistor is typically simply a straight rectangular bar, asshown in Fig 2.1 However, it may at times be better to try different shapes

in order to optimize the overall layout of a circuit A convenient method fordetermining the resistance between two points on any shape is the method ofcurvilinear squares Of course computer-based numerical methods such as thefinite-element technique, can also be used However, using paper and pencil, injust 20 minutes an answer could be obtained to within 10% to 20% accuracy.

A curvilinear rectangle may be defined “as any area which is bounded onopposite sides by two flux lines, and on the other sides by two equipotentiallines .” [4] These rectangles can be divided and subdivided into squares ofever-decreasing size Then, based on Eq (2.8), the total resistance can be found

by counting the squares

Rather than estimating the “squareness” of a curvilinear square, circles can bedrawn between two flow lines using a compass or a template Each curvilinearsquare should have its four sides tangent to the inscribed circle

The curvilinear square method is illustrated in Fig 2.2 The procedure takesthe following form:

1 Draw flow lines between the two electrodes as if water is to travel betweenthe electrodes in a laminar flow The spacing between the two flow lines

is less important than the shape of the flow lines The flow lines shouldintersect the electrodes at right angles

(d )

(b )

4 2

3

1

FIGURE 2.2 (a) Resistor shape with a flow line; (b) addition of tangential circles; (c)

drawing best-fit curvilinear squares; (d) expansion of the fractional curvilinear square from (c).

2 Between two adjacent flow lines, draw a series of circles tangent to theflow lines and to each other.

3 Draw equipotential lines between the circles orthogonal to the flow lines

4 If there is more rectangle left over than the number of circles, fill theremaining part of the rectangle with circles in the orthogonal direction.Continue this until the last rectangle is sufficiently close to becoming asquare

5 Starting with the smallest square, count all the squares in series Invert andadd to the next largest row of squares going in the orthogonal direction.Continue inverting and adding to the next larger row of squares

As Fig 2.2 shows, the first step, in which the smallest squares are added,has the result 2 Step 2 consists in inverting the result of step 1 and adding theremaining series of squares, with the result 12C1 D 1.5 In step 3 the result ofstep 2 is inverted and added to the remaining series of squares At the end of thisstep, the result is 1/1.5 C 2 D 2.67 Finally step 4 gives 1/2.67 C 5 D 5.375.The resistance then in the indicated section of the resistor is 5.375 Ð R
Thesesteps are repeated for the other parallel sections to obtain the total resistance as

a parallel combination

The obvious application of this method to electrical engineers is in finding theresistance of an arbitrarily shaped resistor However, it can also be applied infinding the magnetic reluctance in a magnetic circuit, capacitance, heat convec-tion, and, of course, laminar fluid flow

There are a couple of other details that should be considered in predictingresistance values One is that the rectangular bars of resistance are not reallyrectangular bars The bottom is rounded, and a better estimate can be found bytaking this characterstic into account Another complication is that somewhere asemiconductor diffused resistor is going to have to come in contact with a metal.The resulting Schottky barrier can cause an additional voltage drop Normally anOhmic contact is used for this interface An Ohmic contact is formed by heavilydoping the semiconductor at the point of contact with the metal This essentiallypromotes tunneling of electrons through the barrier Nevertheless, there is stillsome residual resistance from the contact Consequently the previously givenexpression for resistance, Eq (2.8), should be modified to incorporate the contactresistance, Rc:

R D R
L

WC

2Rc

A typical value for Rc is about 0.25 -mm

Active loads are often used in integrated circuits in place of passive loadswhere the required resistance value is fairly high The primary advantage of theactive load is its compact size relative to that of a large passive load Theseare often used in common emitter NPN transistor amplifiers or FET amplifiers

as shown in Fig 2.3 As the figure shows, the base-collector, the gate-drain ofthe enhancement mode FET, and the gate-source of the depletion mode FET are

V i

FIGURE 2.3 Active loads using (a) common emitter structure, (b) p-channel

enhance-ment mode MOSFET load, and (c) n-channel depletion mode MOSFET load.

is simpler to construct than the usual depletion mode FET with the gate shorted

to the source The saturation current in GaAs is reached at a rather low tion field of 3 kV/cm This means that once saturation has occurred, there is asmall increase in the current with each increase in voltage Consequently a largeeffective resistance is obtained The saturated resistor channel depth is effectivelygreater than that of the MESFET channel as shown in Fig 2.4 Consequently,for a given resistance value, the width of the saturated resistor would have to

satura-be made narrower Resistance values of 8 to 10 k have satura-been obtained [5].However, the simpler processing of the saturated resistor has given improvedreliability and repeatability of these devices

2.3 CAPACITORS

Some of the most important parameters that need consideration in choosing

a capacitance are (1) the capacitance value, (2) capacitance value tolerance,(3) loss or Q, (4) temperature stability, (5) mechanical packaging and size,and (6) parasitic inductance These criteria are interdependent, so often theappropriate compromises depend on the constraints imposed by the particularapplication This section will consider both hybrid and monolithic capacitordesigns

2.3.1 Hybrid Capacitors

Hybrid capacitors are available in both single-layer capacitors for high-frequencylow-capacitance applications and multi-layer capacitors for higher capacitance.Even for multilayer chip capacitors, the self-resonant frequency for a 0.1 pFcapacitor is over 10 GHz and for a 1000 pF capacitor the self-resonant frequency

of 250 MHz These capacitors can be attached to hybrid circuit boards to providehigh available capacitances with relatively low loss Unlike low-frequency cir-cuits, certain parasitic circuit elements must be accommodated in the overalldesign The parasitic inductance is affected by the packaging, since it is usuallyassociated with the lead attachments to the capacitor and line length effects insidethe capacitor In low-frequency circuits the effect of the inductance is so small that

it can safely be neglected However, at radio frequencies both the inductance andthe metal losses often become significant Consequently the equivalent circuit for

a chip capacitor as developed by chip capacitor manufactures is shown in Fig 2.5and can sometimes be simplified as simply a series RLC circuit The additionalparallel resistance, Rp is added to this equivalent circuit to model resistive lossescaused by dielectric loss This parameter is the main loss at low frequencies inthe hertz to kilohertz range, but at RF it becomes negligible when compared to

Rs The impedance of the circuit is

where ω0 D1/pLCis the self-resonant frequency

While loss in capacitors is usually less than that in inductors, capacitor losscan still be significant in circuit performance Loss can be described in terms ofdissipation factor (DF), loss tangent (tan υ), the equivalent series resistance (RR s),

and Qcap Since the circuit Q is assumed to result from a series RLC configuration,

EDE2f55.5 Ð 106εrtan υ W/cm3 2.14Some of the most widely used dielectric materials for capacitors are shown inTable 2.2

The BaTiO3, εrD8000, material provides the most compact capacitor ever, it has relatively poor temperature coefficient, tan υ shift with voltage, coef-ficient of expansion in terms of temperature, piezoelectric effects, and agingqualities because of its porosity

How-The BaTiO3, εrD1200, capacitance varies by C15% from 55°C to 125°C.When the BaTiO3 materials are heated to about the Curie point, the value for εrjumps up about 10% to 15% After cooling and waiting 10 hours, the dielectricconstant drops back down only 3% of its peak value, and after 10,000 hours, itdrops down only 7% of its peak value As the voltage changes over a range of

30 V, the loss tangent increases from 0.01 to 0.1 at low frequencies There arefour crystalline phases for BaTiO3 as it is heated up The crystal changes fromorthorhombic to tetragonal to cubic (which is near the Curie point) At each of

TABLE 2.2 Loss Tangent (tan d) of Dielectric Materials

these changes, there is an abrupt change in the mechanical size of the crystal [7].This has deleterious implications on solder joints of the capacitor.

The capacitance using NPO material varies with temperature š30 ppm/°C

It moves in the negative direction, then in the positive direction exceeding theinitial capacitance, and finally settling down near the original capacitance as thetemperature rises Hence it gets the name NPO

The porcelain materials provide high Q, no piezoelectric effects, no agingeffects (since it is not a porous material), and temperature coefficient of

š30 ppm/°C up to 125°C The coefficient of expansion of the porcelain capacitor

is the same as alumina (Al2O3) For this reason, when mounted on an aluminasubstrate, the two will expand the same amount The series resistance at 1 GHzvaries with the value of capacitance as shown in Table 2.3

For a 30-pF BaTiO3, εrD1200, capacitor operating at 300 MHz, the tance can be as high as 1 and result in 0.3-to 3-dB dissipation loss In solidstate circuits that operate in high-current and low-voltage conditions, these lossescan be quite significant The generated heat further degrades the loss tangent,which increases the heat dissipation Thermal runaway can occur, causing self-destruction Of the materials shown in Table 2.2, porcelain provides the best losstangent, especially at frequencies in the 1 to 3 GHz range

resis-The frequency range of a chip capacitor can be extended by the simple dient of turning it on its side (Fig 2.6) Resonances appear to be the result ofdifferent path lengths of the path through the lower plates and upper plates of amulti-layer capacitor Turning the capacitor on its side tends to equalize the pathlengths and eliminates all odd-order harmonic resonances [7]

expe-2.3.2 Monolithic Capacitors

Capacitors in monolithic circuits are best avoided where possible because of theamount of real estate they occupy Nevertheless, they are sometimes required.The capacitance tolerance is typically š10%, and capacitance values range from0.2 to 100 pF There are four types of monolithic capacitors that might be used in

TABLE 2.3 Resistance of Porcelain Capacitors

( a ) ( b )

FIGURE 2.6 Metallic conductors in (a) horizontal and (b) vertical orientation.

monolithic circuit designs: (1) open circuit stub, (2) interdigital line, (3) insulator metal, and (4) varactor diode

metal-The open circuit stub capacitance is simply an open circuit transmission linewhose length is < "/4 The capacitive susceptance is obtained from the trans-mission line equation:

B D Y0tan

ωl

a shunt capacitance to ground While the susceptance is not proportional to ω

as in lumped capacitors, it is a good approximation when the argument of thetangent function is small Line lengths can use a large amount of real estate atlow frequencies, so typically the open stub capacitor is most useful at frequenciesgreater than about 8 GHz

The interdigital capacitor shown in Fig 2.7, unlike the open stub, providesseries capacitance It is most useful for capacitances less than 1 pF, and at 12 to

14 GHz it typically has a Q of 35 to 50 The equivalent circuit shown in Fig 2.7includes series resistance and inductance, as well as some shunt capacitance toground The latter is caused by the metal-insulator-ground metal of the microstripstructure The main series capacitance can be estimated from

C D Nf1Cg& 2.16where Nfis the number of fingers, & is the finger length, and Cg is the static gapcapacitance between the fingers

A third type of capacitor is the metal-insulator-metal capacitor (Fig 2.8) Ofthe four monolithic capacitors, this is the most popular and is the most obvious.The dielectric thickness typically used is 0.1 to 0.4µm Losses can be reduced ifthe metal thickness is greater than two skin depths The metal surface roughnessshould be as smooth as possible to reduce losses and avoid pin holes in thedielectric Typically the capacitance ranges from 50 to 300 pF/mm2 [2] When

FIGURE 2.7 Interdigital capacitor layout and equivalent circuit.

C

Metal

FIGURE 2.8 Metal-insulator-metal capacitor and equivalent circuit.

the conductor losses prevail over the dielectric losses, the conductor quality factor

TABLE 2.4 Monolithic Capacitor Dielectric Materials

Dielectric Nominal εr Range of εr Temperature

The fourth way of obtaining capacitance is by means of the junction tance of a Schottky diode This capacitance is

capaci-C D C0

where ) ³ 1/2 [8, p 190] When the applied voltage, V, is zero, the capacitance

is C0 A major disadvantage of this capacitance is its voltage dependence relative

to the built-in potential, (

2.4 INDUCTORS

Inductors operating at radio frequencies have a variety of practical limitationsthat require special attention A tightly wound coil in addition to providing a selfinductance also has heat loss due to the nonzero wire resistance, skin effect losses,eddy current losses, and hysteresis losses when a magnetic material is used.Furthermore two conductors close together at two different voltages will alsoexhibit an interelectrode capacitance At radio frequencies these effects cannot

be neglected as easily as they could at lower frequencies The equivalent circuit isshown in Fig 2.9 In this figure the series resistance, Rs, represents the conductorloss as well as the skin effect losses The parallel resistance, Rp, representsthe effect of eddy current losses and the hysteresis loss in magnetic materialswhen present The shunt capacitance, C, is the capacitance found between thecoils Straightforward circuit analysis gives the impedance for this equivalentcircuit:

Z D RpRsCRpLs

s2LCR CsRCR CL C RR 2.21

INDUCTORS 21

FIGURE 2.9 Simple equivalent circuit for an inductor.

If Rpis considered so large as to have negligible effect, and if the remaining seriescircuit Q D 1/ωRsCis large, then the effective inductance is approximately

induc-RF inductor and some design methods for induc-RF inductors

2.4.1 Resistance Losses

The dc current flowing through a wire with a cross-sectional area, A, will ter twice the resistance if the area is doubled At radio frequencies the ac currenttends to flow near the surface of the conductor because of the skin effect Thiscan be illustrated by an electric field impinging on a conductor whose resistance

encoun-is not zero The field will penetrate into the conductor and will exponentiallydecay as it penetrates deeper:

Ex D E0ex/υ 2.24where

υ D



In this equation f is the frequency, is the resistivity, and  is the permeability.Because of this skin depth, the resistance of a given wire with radius R willhave a higher resistance at high frequencies than at dc The ac resistance is given

by [9]

RACD Atot

A Rdc

TABLE 2.5 Common Conductors

/R22/υR  /υ2

The possibility for Rac to be infinite or even negative clearly indicates that

Eq (2.26) has gone beyond its range of applicability The problem is that theskin depth has become greater than twice the wire radius Listed in Table 2.5 arethe resistivities and skin depths of a few common metals

Another important loss mechanism is called the proximity effect When one

conductor supporting a changing magnetic field is brought close to anotherconductor, currents will be induced on the second conductor in conformity with

Faraday’s law These currents are called eddy currents, and they flow in closed

paths so as to produce a magnetic field that is in opposition to the originally

applied external field These currents produce Joule heating This is exactly the

condition that occurs in a tightly wound inductive coil When many wires areclose together, the loss problem is compounded, and the eddy current losses can

be quite significant As an illustration of this, consider a coil with length to eter ratio of 0.7 If this coil is unwound and laid out as a straight wire, the losseswill drop by a factor of 6 [9, p 47]

in comparison with most other magnetic materials The relative permeability for